In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If ∠APQ = 58° then the measure of ∠PQB is

Question

In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If ∠ APQ = 58° then the measure of ∠ PQB is

Philoid · Accepted Answer

In the given Figure, Join OP

Now, OP ⏊ AB

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

∴∠OPA = 90°

∠OPQ + ∠APQ = 90°

∠OPQ + 58° = 90°

[Given, ∠APQ = 58°]

∠OPQ = 32°

In △OPQ

OP = OQ

[Radii of same circle]

∠OQP = ∠OPQ

[Angles opposite to equal sides are equal]

∠PQB = 32°

[As ∠OQP = ∠PQB ]